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You seem to have a very narrow definition of "decentralized system."
In the future I imagine nodes might probabilistically check a random subset of transactions, and broadcast "this transaction is fraudulent" if they find anything wrong. If you imagine a million nodes, each fully validating one-in-ten-thousand transactions then you get each transaction validated on average 100 times.
That's not so different from your 'treechains' idea (just simpler and easier to reason about, in my humble opinion).
If you think that hardware costs are going to dominate decentralized-versus-centralized payment network costs, then I think you're wrong. Hardware is cheap, people are expensive.
But all of this is really arguing angels-dancing-on-the-heads-of-pins; we've got years before we have to worry about how to fund network security, and a whole lot of things to work on before then.